to 



Transverse Strain in Beami 



411 



passed the neutral axis will be displaced to a small extent from 

 the centre of gravity of the section. 



In the case of cast iron it has been found, as already stated, 

 that even with very moderate strains the ratio of stress to 

 strain varies to some extent from its initial value E. But 

 this variation does not become considerable for either 

 tensile or compressive stress until it approaches that which 

 ultimately produces rupture*. And no very considerable 

 error will result from assuming that the compressive stress 

 varies directly with the strain in any bar of rectangular section 

 subjected to transverse strain, and that the tensile stress also 

 varies directly with the strain until it reaches the amount 

 which ultimately produces rupture and then remains constant 

 until the strain likewise reaches the point of rupture. 



These assumptions will simplify the figures, the areas of 

 which measure the total tensile or compressive stress, and 

 these will then become respectively the pentagonal figure 



I -A 



B K 



"\__ 





k^^ 





2>^ 







^> 



< ^G 





M 



V ^^ N 



V 



/ 



P ^\ S 







\ 





TQV 

 Fy 8. 



D 



CLHMD and the triangle I H K, the dimensions of which 

 may be readily computed. 



Make HO (fig. 8)=i depth and ON and P each = £ 

 width of the beam. 



Then if NP be taken to represent the maximum tensile 

 stress, S, or a little less than the tensile breaking-stress, pro- 

 duce this line to R and S (equidistant from 0) , and assume 

 R S to represent on a scale E times as great the elongation of 

 the fibres at a depth below the neutral axis equal to half the 

 depth of the beam. 



Draw straight lines through H R, H S, intersecting verticals 

 through N and P in L and M, and produce them in both 



* It appears from the experiments of Mr. Hodgkinson that the break- 

 ing compressive stress of cast iron is generally from 100,000 to 130,000 lb. 

 -Phil. Trans. (1857) p. 866. 



